Self-consistent strong screening applied to thermonuclear reactions

TL;DR

This paper models strong plasma screening effects during Big Bang nucleosynthesis by solving the non-linear Poisson-Boltzmann equation with Fermi-Dirac statistics, revealing minor overall effects but significant impact on high-Z element fusion rates.

Contribution

It introduces a self-consistent method to calculate strong plasma screening in BBN, incorporating Fermi-Dirac statistics and finite nuclear size effects, which refines previous models.

Findings

Screening effects are minor at high temperatures but can enhance high-Z fusion rates.

Fermi-Dirac statistics are essential near nuclear surfaces where work energy is significant.

Spatial dependence of the screening potential is pronounced near the nuclear surface.

Abstract

Self-consistent strong plasma screening around light nuclei is implemented in the Big Bang nucleosynthesis (BBN) epoch to determine the short-range screening potential, $e\phi(r)/T \geq 1$, relevant for thermonuclear reactions. We numerically solve the non-linear Poisson-Boltzmann equation incorporating Fermi-Dirac statistics adopting a generalized screening mass to find the electric potential in the cosmic BBN electron-positron plasma for finite-sized $^4$He nuclei as an example. Although the plasma follows Boltzmann statistics at large distances, Fermi-Dirac statistics is necessary when work performed by ions on electrons is comparable to their rest mass energy. While strong screening effects are generally minor due to the high BBN temperatures, they can enhance the fusion rates of high-$Z>2$ elements while leaving fusion rates of lower-$Z\le 2$ elements relatively unaffected. Our results also reveal a pronounced spatial dependence of the strong screening potential near the nuclear surface. These findings about the electron-positron plasma's role refine BBN theory predictions and offer broader applications for studying weakly coupled plasmas in diverse cosmic and laboratory settings.